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Original Articles

Bilevel derivative-free optimization and its application to robust optimization

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Pages 561-577 | Received 23 Mar 2010, Accepted 03 Dec 2010, Published online: 17 Oct 2011

References

  • Bandeira , A. , Scheinberg , K. and Vicente , L. N. 2011 . Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization , in preparation
  • Bard , J. F. 1998 . Practical Bilevel Optimization: Algorithms and Applications , Dordrecht : Kluwer Academic Publishers .
  • Bertsimas , D. , Nohadani , O. and Teo , K. M. 2010 . Robust optimization for unconstrained simulation-based problems . Oper. Res. , 58 : 161 – 178 .
  • Cascon , A. , Keating , C. and Shadwick , W. 2002 . “ The Omega function ” . In Tech. Rep , London : The Finance Development Centre .
  • Case , L. M. 1997 . “ An l1 penalty function approach to the nonlinear bilevel programming problem ” . Canada : University of Waterloo . Ph.D. thesis
  • Conn , A. R. , Scheinberg , K. and Toint , Ph. L. 1997 . “ On the convergence of derivative-free methods for unconstrained optimization ” . In Approximation Theory and Optimization , Edited by: Powell , M. D. , Buhmann , A. and Iserles . 83 – 108 . Cambridge : Cambridge University Press . Tributes to M.J.D.
  • Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 2000 . Trust-Region Methods Philadelphia MPS-SIAM Series on Optimization, SIAM
  • Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2008 . Geometry of interpolation sets in derivative free optimization . Math. Program. , 111 : 141 – 172 .
  • Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2009 . Global convergence of general derivative-free trust-region algorithms to first and second order critical points . SIAM J. Optim. , 20 : 387 – 415 .
  • Conn , A. R. , Scheinberg , K. and Vicente , L. N. 2009 . Introduction to Derivative-Free Optimization , Philadelphia : SIAM . MPS-SIAM Series on Optimization
  • Dempe , S. 2002 . Foundations of Bilevel Programming , Dordrecht : Kluwer Academic Publishers .
  • Fasano , G. , Morales , J. L. and Nocedal , J. 2009 . On the geometry phase in model-based algorithms for derivative-free optimization . Optim. Methods Softw. , 24 : 145 – 154 .
  • Kane , S. J. , Bartholomew-Biggs , M. C. , Cross , M. and Dewar , M. 2009 . Optimizing Omega . J. Global Optim. , 45 : 153 – 167 .
  • Minsky , B. , Obradovic , M. , Tang , Q. and Thapar , R. 2009 . Applying a global optimisation algorithm to fund of hedge funds portfolio optimisation .
  • Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
  • Powell , M. J.D. 2004 . Least Frobenius norm updating of quadratic models that satisfy interpolation conditions . Math. Program. , 100 : 183 – 215 .
  • Shimizu , K. , Ishizuka , Y. and Bard , J. F. 1997 . Nondifferentiable and Two-Level Mathematical Programming , Boston : Kluwer Academic Publishers .

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